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Let $D_n \subseteq \Sigma_n$ be the set of derangements in the symmetricgroup. We prove that the complex of injective words generated by $\Sigma_n\setminus D_n$ is contractible. This gives a conceptual explanation to the wellknown fact that the complex of injective words generated by $\Sigma_n$ ishomotopy equivalent to the wedge sum $\underset{|D_n|}{\bigvee} S^{n-1}$.

The complex of injective words of permutations which are not derangements is contractible